The cockpit of a plane is covered with snow in Luton airport. Photograph: Oli Scarff/Getty Images

More snow, freezing fog and temperatures below -9C in parts of England and -15C in the Scottish Highlands overnight caused continued havoc on the roads and railways and at airports today.

The icy conditions contributed to a spate of accidents, including a coach crash in Cornwall that killed two people and injured 47.

A Ryanair passenger jet from Dublin slid off the runway at Glasgow's Prestwick airport after hitting a patch of ice just after 9am. No one was injured, but Strathclyde Fire and Rescue were at the scene as a precaution.

Elsewhere, air traffic controllers restricted flights at Heathrow because of fog, Southampton runway was closed because of ice, and 36 easyJet flights were cancelled.

On the roads, the AA attended 3,000 breakdowns between midnight and 9am.

A section of the A27 in East Sussex was closed after an accident and part of the A66 in Cumbria was shut. In Dorset, up to 20 cars were involved in accidents caused by ice on the A35 Tolpuddle bypass near Bere Regis.

Hampshire police reported six accidents last night and this morning on the M27, where some lorry drivers were forced to pull on to the hard shoulder because it was too dangerous to continue. The county had been badly hit by snow, compounded last night by a severe freeze. The Hampshire village of Odiham recorded England's lowest temperature of -9.6C.

Up to 12 million people are expected to travel to family and friends today and tomorrow for Christmas, according to the AA. The Met Office has issued several warnings of "widespread icy roads" for most of England, Scotland and Northern Ireland.

The RAC said those travelling by car for Christmas should consider delaying their journeys, given the slightly warmer conditions on the way.

Buses replaced trains on Southeastern services between Sittingbourne and Sheerness-on-Sea, and Strood and Paddock Wood in Kent, and between Fareham and Havant in Hampshire. A broken-down train at Dunton Green in Kent led to long delays between Sevenoaks and Orpington in the morning rush hour.

The company was unable to run trains between the Kent stations of Tunbridge Wells and Hastings, Faversham and Dover Priory, Ramsgate and Dover Priory and Otford and Maidstone East. Because of poor road conditions, there were no replacement buses on these routes.

In Sussex, services run by the Southern train company were cancelled, including some between London and Brighton and between Brighton and Lewes.

Bob Crow, the general secretary of the Rail Maritime and Transport union, said: "A combination of greedy train operating companies cutting corners to maximise their profits, alongside Network Rail maintenance cuts, has created conditions where as soon as there is bad weather the railway system collapses into chaos."

In Scotland, there were rush-hour delays between Glasgow Central and Edinburgh and Lockerbie. Edinburgh city centre was brought to a standstill by blizzard conditions.

A spokesman for Lothian and Borders police said: "It is chaos at the moment. We would urge people to stay off the roads until it clears."

Tulloch Bridge in the highlands was Britain's coldest place last night at -15.2C.

There was better news from Eurostar, which has cleared the backlog of stranded passengers after three days of cancelled services. The company is operating about two-thirds of its normal service today. Passengers who intend to travel today are advised not to go to Eurostar's London terminal at St Pancras International until after 1pm.

British Airways said fog at Heathrow airport caused the cancellation of some short-haul flights, but its Gatwick flights were operating normally.

More flights than expected were operating at Manchester airport after anticipated heavy snowfall failed to materialise overnight.